Approximating discrete valuation rings by regular local rings

Authors:
William Heinzer, Christel Rotthaus and Sylvia Wiegand

Journal:
Proc. Amer. Math. Soc. **129** (2001), 37-43

MSC (1991):
Primary 13F30, 13H05; Secondary 13E05, 13G05, 13J05, 13J15

DOI:
https://doi.org/10.1090/S0002-9939-00-05492-7

Published electronically:
July 27, 2000

MathSciNet review:
1694346

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a field of characteristic zero and let be a discrete rank-one valuation domain containing with . Assume that the fraction field of has finite transcendence degree over . For every positive integer , we prove that can be realized as a directed union of regular local -subalgebras of of dimension .

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Additional Information

**William Heinzer**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395

Email:
heinzer@math.purdue.edu

**Christel Rotthaus**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027

Email:
rotthaus@math.msu.edu

**Sylvia Wiegand**

Affiliation:
Department of Mathematics and Statistics, University of Nebraska, Lincoln, Nebraska 68588-0323

Email:
swiegand@math.unl.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05492-7

Keywords:
Discrete rank-one valuation domain,
\'{e}tale extension,
excellent ring,
Henselization,
local uniformization,
regular local domain

Received by editor(s):
July 23, 1998

Received by editor(s) in revised form:
March 22, 1999

Published electronically:
July 27, 2000

Additional Notes:
The authors thank the National Science Foundation and the National Security Agency for support for this research. In addition they are grateful for the hospitality and cooperation of Michigan State University, the University of Nebraska and Purdue University, where several work sessions on this research were conducted.

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 2000
American Mathematical Society